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" In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... "
Elementary text-book of trigonometry - Side 118
av Robert Hamilton Pinkerton - 1884 - 176 sider
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Introduction to Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - 1905 - 217 sider
...• ] ji j14. sin2x = 2 sinx cos x ; cos 2 ж = cos2x — sin2x ; tan2x = 16. Theorem. Law of sines. In any triangle the sides are proportional to the sines of the opposite angles; abc that is, - — r = ^-;; = ^-^sm A sin В sm С 17. Theorem. Law of cosines. In any triangle the...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - 1906
...naming the sides and angles of a triangle, see Plane Trigonometry, Part 1. 18. Principle of Sines. — In any triangle, the sides are proportional to the sines of the opposite angles. That is, a. _ sin A a _ sin A .b sin R b sin B1 c sin C' c sin C Let ABC, Fig. 6, be any triangle and...
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Plane Trigonometry

1906 - 188 sider
...the sides and angles of a triangle, see Plane Trigonometry, Part 1. 18. Principle of Sines. — fn any triangle, the sides are proportional to the sines of the opposite angles. That is, a _ sin A a _ sin A b, _ sin B b sin B^ c sin C' c sin C Let ABC, Fig. 6, be any triangle...
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A First Statics

Charles Samuel Jackson, Robert Moir Milne - 1907 - 372 sider
...Lami's theorem is the translation into a statical proposition of the trigonometrical proposition that in any triangle the sides are proportional to the sines of the opposite angles. c Resolving. — If ABC is any A and AA', BB' and CC' are drawn perpendicular on any straight line...
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A Text-book on Advanced Algebra and Trigonometry, with Tables

William Charles Brenke - 1910 - 343 sider
...to obtain. Additional relations will then be derived from these. The Law of Sines. — In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle, CD one of its altitudes. Two cases arise, according as D falls within or without the...
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Elements of Applied Mathematics

Herbert E. Cobb - 1911 - 274 sider
...perpendicular from A to a we may obtain, in a similar manner, sin C sin B bc sin A sin B sin C LAW OF SINES. In any triangle the sides are proportional to the sines of the opposite angles. When a side and two angles of a triangle are given we may find the other two sides by this law. PROBLEMS...
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Plane and Sperical Trigonometry (with Five-place Tables): A Text-book for ...

Robert Édouard Moritz - 1913 - 520 sider
...sin С. (г) Equation (i) or (2) embodies what is known as the Law of Sines, which states that, — In any triangle the sides are proportional to the sines of the opposite angles. (b) Second proof. The Law of Sines may be proven in another way, which at the same time brings out...
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Shop Mathematics ...: Advanced shop mathematics

Earle Bertram Norris, Kenneth Gardner Smith, Ralph Thurman Craigo - 1913
...written in the following form : abc sin A - sin B- sin C Written in words this would be as follows: "In any triangle, the sides are proportional to the sines of the angles opposite them." 139. Application of Laws to Problems. — There may be four possible cases of...
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Manual of Petrographic Methods

Albert Johannsen - 1914 - 649 sider
...incidence, F'iAM = r= the angle of refraction, and Ri = AM = the radius of curvature of the lens. Since in any triangle the sides are proportional to the sines of the opposite angles, we have, in the triangle MAFiM: (i) i ART. 85] LENSES 117 and in the triangle MAF'\M sin r _ sinr_...
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PLANE TRIGONOMETRY WITH TABLES

CLAUDE IRWIN PALMER - 1914
...derived from the formulas growing out of the sine theorem and cosine theorem. 76. Sine theorem. — In any triangle the sides are proportional to the sines of the opposite angles. First proof. In Fig. 81, let ABC be any triangle, and let h be the perpendicular from B to AC. The...
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